Worksheet Worksheets

Learning Objectives

• Explain how sampling variability affects sample statistics and uncertainty in conclusions
• Interpret confidence intervals and explain what they mean (and do not mean)
• Use sample size and estimates (e.g., p̂) to compute standard error and confidence intervals

Learning Objectives

• Interpret a quotient involving a fraction divided by a whole number using equal-size grouping.
• Interpret a quotient involving a whole number divided by a fraction as how many fractional-sized groups fit.
• Use multiplication to check division answers (divisor × quotient = dividend).+ Show more

Learning Objectives

• Interpret a percent as a part out of 100 and connect it to equivalent decimals.
• Convert between percent form and decimal form for rational numbers.
• Use number lines and bar (tape) models to locate equivalent percent/decimal values.

Learning Objectives

• Explain why opposite rational numbers are the same distance from 0 using absolute value
• Find absolute values for positive and negative rational numbers shown on a number line
• Use opposite relationships to compare absolute values and distances on a number line

Learning Objectives

• Read and interpret rational numbers as points on a number line, relative to 0.
• Use the number line to compare rational numbers and describe their positions (left/right of 0).
• Find distances between points and from 0 using absolute value ideas.

Learning Objectives

• Interpret inequalities using the direction of shading (left/right) on a number line
• Identify whether an endpoint is included by using open vs closed circles
• Write an inequality from a number line graph (and vice versa) using rational numbers

Learning Objectives

• Convert fractions to terminating decimals and relate them to equivalent decimals on a number line.
• Convert between fractions, decimals, and percents for the same rational value.
• Recognise when a fraction will have a terminating decimal and connect repeating decimals to fraction form.

Learning Objectives

• Interpret a fraction division statement (a/b) ÷ (c/d) as how many copies of (c/d) fit into (a/b)
• Use a tape diagram to represent fraction division and determine the quotient
• Solve simple equations that model fraction division as repeated equal-size pieces+ Show more

Learning Objectives

• Translate real situations into probability models using clear assumptions about the sample space and equally likely outcomes
• Use probability models to compute likelihoods, including complements
• Compare scenarios by using the probability model outcomes rather than intuition+ Show more

Learning Objectives

• Read dot plots, histograms, and box plots to identify key features such as shape, center, and spread
• Interpret one-to-one scales by connecting visual features (median, quartiles, bar heights) to quantitative meaning
• Distinguish typical values from extreme values (outliers) using graphical information and the 1.5×IQR rule

Learning Objectives

• Use the unit circle to determine the signs of sine and cosine in each quadrant
• Convert between angle measures and the corresponding sine/cosine values using reference angles
• Model periodic behavior by interpreting amplitude, period, and phase shift in sine and cosine functions

Learning Objectives

• Evaluate exact trigonometric values for common radian angles using the unit circle.
• Determine the signs of sine, cosine, and tangent based on the quadrant.
• Use radian angle relationships and periodicity to find equivalent trig values.

Learning Objectives

• Understand that converting a decimal to a percent means multiplying by 100
• Convert decimals (including decimals greater than 1) into percents
• Relate the size of a decimal to the size of its percent value

Learning Objectives

• Interpret what an input–output statement like f(a)=b means in a real context
• Connect the same function meaning across equations, tables, and graphs
• Distinguish between the input value (a) and the output value (b) when reading function notation

Learning Objectives

• Compare exponential and linear models by evaluating them at multiple input values
• Identify how multiplicative (exponential) growth differs from additive (linear) growth
• Find and interpret the crossover point where an exponential model overtakes a linear model+ Show more

Learning Objectives

• Interpret the parameters a and b in an exponential model y=a·b^x
• Determine whether an exponential function represents growth or decay from the value of b
• Use a and b to predict values of a function at different time steps

Learning Objectives

• Write composed functions using the correct order (f ∘ g)(x) = f(g(x)).
• Evaluate composed function models by substituting one function into another.
• Interpret composed models as multi-step processes where one output becomes the next input.+ Show more

Learning Objectives

• Solve polynomial equations that have no real solutions by using complex numbers
• Use the facts i² = −1 and complex arithmetic to find and verify complex solutions
• Interpret solutions as roots of factored forms of polynomials involving i

Learning Objectives

• Expand products of complex numbers of the form (a + bi)(c + di) using distributive multiplication.
• Simplify expressions using i^2 = −1 and collect like terms to write answers in the form x + yi.
• Identify real and imaginary parts after complex multiplication.+ Show more

Learning Objectives

• Express complex numbers in the form a + bi and identify the real part a and imaginary coefficient b
• Rewrite expressions involving i into standard complex form a + bi
• Interpret and use the values of a and b to understand properties of complex numbers+ Show more

Learning Objectives

• Factor quadratics with no real roots into linear factors over the complex numbers using conjugate pairs
• Use completing the square to find complex roots and write the corresponding conjugate linear factors
• Expand and simplify products of conjugate linear factors to recover the original quadratic

Learning Objectives

• Add complex numbers by combining like terms (real parts with real parts, imaginary parts with imaginary parts).
• Use the associative and distributive ideas to regroup complex numbers without changing the sum.
• Write sums in the standard form a+bi and interpret the real and imaginary components.

Learning Objectives

• Write complex numbers in standard form a + bi and identify the real part a and imaginary part b
• Simplify expressions involving i using i^2 = -1
• Add and multiply complex numbers by combining real and imaginary parts correctly

Learning Objectives

• Find the conjugate of a complex number and use it to rationalise denominators in division
• Simplify complex-number quotients into standard form a+bi by eliminating the imaginary part of the denominator
• Identify the real and imaginary parts of a quotient after conjugate multiplication

Learning Objectives

• Use unit conversion factors written as ratios to cancel unwanted units
• Convert quantities that include derived units (e.g., speed, density, area, volume per time)
• Apply a multi-step conversion chain while keeping units consistent throughout

Learning Objectives

• Choose appropriate quantities and definitions so that a model’s calculated values represent the intended measurements.
• Read and interpret values accurately from absolute value graphs and linear inequality graphs used in quantity modeling.
• Justify whether a given point or computed value is consistent with a model (including strict vs inclusive conditions).

Learning Objectives

• Convert between radical notation and rational exponent notation using a^(1/n)=ⁿ√(a)
• Rewrite expressions like √(a^m) and ∛(a^m) as a^(m/n) (and vice versa) using exponent rules
• Simplify expressions by applying rational exponent laws after conversion+ Show more

Learning Objectives

• Find the coordinate distance between two points that are horizontally or vertically aligned on a coordinate plane.
• Use the absolute difference of the changing coordinate values to calculate distance.
• Read point coordinates from a grid and apply the coordinate distance rule correctly.

Learning Objectives

• Calculate the surface area of a right rectangular prism by adding the areas of matching face pairs.
• Use the formula SA = 2(lw + lh + wh) for edge lengths l, w, and h.
• Apply the same multiplication structure when one or more side lengths are fractional.

Learning Objectives

• Translate word constraints (at most, at least, less than, greater than) into inequalities.
• Interpret a graph or number line to determine which values satisfy an inequality, including whether the boundary value is included.
• Write solution sets using interval notation for inequalities.

Learning Objectives

• Compare two data distributions using their center, spread, and shape.
• Interpret how differences in mean/median and measures of spread (range/IQR) affect conclusions.
• Use skewness and outliers to explain why summary statistics may differ between two data sets.

Learning Objectives

• Explain how random sampling and sampling variability affect statistical conclusions.
• Distinguish between a population parameter and a sample statistic when making inferences.
• Interpret confidence intervals as estimates that reflect uncertainty, not exact values.+ Show more

Learning Objectives

• Identify the role of coefficients and constant terms in algebraic expressions
• Explain how each part of an expression affects the overall value in context
• Use structure (addition and multiplication in particular) to simplify and interpret expressions+ Show more

Learning Objectives

• Explain how compound interest depends on both the interest rate and the length of time
• Use percentage models to find interest (a percent of a balance) and the new balance
• Solve simple linear equations that arise when working backward to find a missing savings amount+ Show more

Learning Objectives

• Use estimation to judge whether a financial decision is reasonable
• Compare options using calculations and reasonableness checks
• Use inequalities to decide if spending fits within a budget+ Show more

Learning Objectives

• Use ratio reasoning (tape diagrams) to split limited resources fairly.
• Use unit value to convert between ratios and actual amounts of money/time.
• Write and interpret inequalities that represent resource limits (at most/at least).+ Show more

Learning Objectives

• Interpret discounts, sales, and per-unit prices to compare value between options.
• Calculate savings and sale prices using proportional reasoning.
• Use ratios and tables to decide which purchase is the better buy.

Learning Objectives

• Translate real situations into equations/inequalities using two variables.
• Interpret how changing one variable affects the other in a two-variable model.
• Graph linear inequalities in two variables by describing which side of the boundary line to shade.+ Show more

Learning Objectives

• Use inverse operations to follow and justify step-by-step equation-solving algorithms
• Check whether a proposed output from an algorithm is correct by substituting back into the original rule
• Translate simple algorithm descriptions into algebraic expressions and compute results+ Show more

Learning Objectives

• Expand algebraic expressions using the distributive property
• Simplify expressions by combining like terms
• Factor expressions into equivalent forms when appropriate+ Show more

Learning Objectives

• Create and interpret graphs that model real-world situations using ordered pairs and linear patterns.
• Use graphs to find key features such as the rate of change (slope) and starting value (y-intercept).
• Solve linear equations and relate the algebraic solution back to a model.+ Show more

Learning Objectives

• Identify the slope and y-intercept from points on a line in a coordinate grid.
• Write a linear function equation y = mx + b from two points.
• Use linear models to make predictions from the graph (including slope meaning).+ Show more

Learning Objectives

• Identify the rule that generates terms in a numeric pattern
• Use algebraic expressions to describe linear and geometric pattern rules
• Translate between a pattern rule and a condition using inequalities+ Show more

Learning Objectives

• Use equations to model and solve real-world situations
• Interpret and read information from coordinate grids and line plots
• Use models to make predictions, and evaluate when a model might be limited

Learning Objectives

• Translate word phrases into algebraic expressions using symbols and variables
• Simplify expressions by expanding brackets using the distributive property
• Recognize when two expressions or equations are equivalent

Learning Objectives

• Combine like terms to simplify algebraic expressions
• Use the distributive property to simplify expressions
• Factor out a common factor to rewrite expressions in simpler equivalent forms+ Show more

Learning Objectives

• Translate real situations into inequalities that describe feasible (allowed) variable values.
• Interpret the meaning of solutions by checking whether candidate points satisfy all constraints at once.
• Use boundary cases (where equality holds) correctly for both strict and inclusive inequalities.+ Show more

Learning Objectives

• Rearrange algebraic formulas to isolate a chosen variable using inverse operations.
• Maintain algebraic equivalence by performing the same operation to both sides of an equation.
• Substitute into rearranged formulas accurately and interpret results using constraints (e.g., non-zero denominators, non-negative roots).